Rewrite as a simplified fraction. ${0.7\overline{41} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 741.4141...\\ 10x &= 7.4141...\end{align*}}$ Subtracting the two equations, we have: ${990x = 734}$ ${x = \dfrac{734}{990}} $ ${x = \dfrac{367}{495}} $